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6 Nov 2019
(1 point) Calculate the circulation, Jc F dr, in two ways, directly and using Stokes' Theorem. The vector field F- (7z - 5y +2z)(i +j) and C is the triangle with vertices (0, 0, 0), (7, 0, 0), (7, 4, 0), traversed in that order Calculating directly, we break C into three paths. For each, give a parameterization On C1 from (0, 0, 0) to (7, 0, 0).à¸à¸µ t)-| On C2 from (7, 0, 0) to (7,4,0), à¸à¸µà¹(t)-| On Gs from (7,4,0) to (0, 0, 0) , à¸à¸µà¹(t)-| (t) that traverses the path from start to end for 0 t1 So that, integrating, we have JoF dF171.5 F dr 156 C2 a F.dr159.5 Ca and so Jc F dr 487 Using Stokes' Theorem, we have curl F - So that the surface integral on S, the triangular region on the plane enclosed by the indicated triangle, is dy dz, where a b- , and d integrating, we get F dF s curl F dA- Show transcribed image text
(1 point) Calculate the circulation, Jc F dr, in two ways, directly and using Stokes' Theorem. The vector field F- (7z - 5y +2z)(i +j) and C is the triangle with vertices (0, 0, 0), (7, 0, 0), (7, 4, 0), traversed in that order Calculating directly, we break C into three paths. For each, give a parameterization On C1 from (0, 0, 0) to (7, 0, 0).à¸à¸µ t)-| On C2 from (7, 0, 0) to (7,4,0), à¸à¸µà¹(t)-| On Gs from (7,4,0) to (0, 0, 0) , à¸à¸µà¹(t)-| (t) that traverses the path from start to end for 0 t1 So that, integrating, we have JoF dF171.5 F dr 156 C2 a F.dr159.5 Ca and so Jc F dr 487 Using Stokes' Theorem, we have curl F - So that the surface integral on S, the triangular region on the plane enclosed by the indicated triangle, is dy dz, where a b- , and d integrating, we get F dF s curl F dA-
Show transcribed image text Jean KeelingLv2
6 Nov 2019